## Section 2.8: Exploring the Twin Paradox

View from Earth-Bound Twin | Pulses from Earth-Bound Twin | Pulses from Traveling Twin | Pulses from Traveling Twin: ST

Please wait for the animation to completely load.

In this Exploration we will be considering different aspects of the so-called twin paradox. Restart. At *t* = 0 years the traveling twin (represented by the green circle) heads out on her journey and then returns at *t* = 10 years **(position given in lightyears)**. In the top panel the spacetime diagram for the stationary frame is shown.

Select View from Earth-Bound Twin and play.

- How fast is the moving twin traveling relative to the stationary twin (measured in
*c*)? - What is 1/slope of the red and green worldlines, respectively?

Select Pulses from Earth-Bound Twin and play. The two twins have agreed to send each other a light pulse once a year on the anniversary of the traveling twin's departure. Also shown is the stationary twin's clock and tick marks on the spacetime diagram depict the sending of the stationary twin's light pulse.

- What is the frequency of the stationary twin's light pulse?
- How many light pulses reach the moving twin during her outbound trip? During her inbound trip?
- At the end of the trip how old is the stationary twin?

One of the most important concepts in special relativity is the idea of the spacetime interval. The spacetime interval is (Δ*s*)^{2} =
c^{2}(Δ*t*)^{2} − (Δ*x*)^{2 }which can be thought of as the Pythagorean theorem of spacetime.

Select Pulses from Traveling Twin and play. Now we have added the traveling twin's clock and numbers on the spacetime diagram to mark the arrival of the traveling twin's light pulse. After you watch this animation, select Pulses from Traveling Twin: ST which adds the traveling twin's light pulses to the spacetime diagram.

- Calculate the spacetime interval for the stationary twin during the animation.
- Calculate the spacetime interval for the traveling twin's outbound trip.
- Calculate the spacetime interval for the traveling twin's inbound trip.
- Compare the sum of (g) and (h) to (f). Why is there this difference?

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